Last Updated on May 11, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We are given that the sum of 4 different odd integers is 64 and need to determine the value of the greatest of these integers.
Statement One Alone:
The integers are consecutive odd numbers
Since we know that the integers are consecutive odd integers, we can denote the integers as x, x + 2, x + 4, and x + 6 (notice that the largest integer is x + 6).
Since the sum of these integers is 64, we can create the following equation and determine x:
x + (x + 2) + (x + 4) + (x + 6) = 64
4x + 12 = 64
4x = 52
x = 13
Thus, the largest integer is 13 + 6 = 19.
Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
Of these integers, the greatest is 6 more than the least.
Using the information in statement two, we can determine that the four integers are consecutive odd integers. Let’s further elaborate on this idea. If we take any set of four consecutive odd integers, {1, 3, 5, 7}, {9, 11, 13, 15}, or {19, 21, 23, 25}, notice that in ALL CASES the greatest integer in the set is always 6 more than the least integer. In other words, the only way to fit two odd integers between the odd integers n and n + 6 is if the two added odd integers are n + 2 and n +4, thus making them consecutive odd integers. Since we have determined that we have a set of four consecutive odd integers and that their sum is 64, we can determine the value of all the integers in the set, including the value of the greatest one, in the same way we did in statement one. Thus, statement two is also sufficient to answer the question.
Answer: D
